Baseball Dad -- setting the speed of a pitching machine

[gr8tnezz]

Homework Statement:: I'm trying to figure out what miles per hour setting I need to use to simulate a pitched baseball traveling 50 miles per hour from a distance of 46 feet. I need to know the equivalent speed setting on a pitching machine to simulate the same speed at a distance of 36 feet. Obviously, to have the same effect on the batter standing 36 feet away instead of 46 feet away, the speed will need to be adjusted lower than 50 miles per hour. It has ten feet less to travel before reaching the batter so 50 mph at 36 feet will look a whole lot faster than 50 mph at 46 feet. SO what formula do I use to calculate proper speed adjustments for the shorter difference?
Relevant Equations:: I have no idea.

velocity and distance

[Moderator's note: moved from a homework forum.]

 

[.Scott]

From BostonBaseball.com (what better source):

the "muzzle velocity" of a pitched baseball slows down about 1 mph every 7 feet after it leaves the pitcher's hand

 

[jbriggs444]

Is the idea to give the batter the same amount of time to react? So same time-in-flight from launch to crossing the plate?

 

[gr8tnezz]

Yes Jbriggs. The problem is the distance on the field from the pitchers mound to home plate is 46 feet in little league. The top kids throw about a 50 mph fastball in 10 year old leagues. So excluding the reality that 50 mph is the top speed, not a constant speed as Scott correctly points out, I’m trying to figure out how best to simulate the reaction time for that speed and distance inside a batting cage that is only 36 feet from launch point of the machine to where the batter is standing 36 feet away. The only thing I have been able to determine for now is converting MPH to feet per second. AT that point, I have exhausted my physics knowledge :)

 

[gr8tnezz]

I suppose that one would calculate the time it takes for an object to travel 46 feet @50mph. And then calculate the speed variable for an object to travel 36 feet to match the same time interval discovered in the first equation.

 

[gr8tnezz]

I think the answer is 38 mph. Setting the machine at 38 mph will cause the ball to arrive at home plate in .627 seconds at 36 feet. A pitched ball at 50 mph will arrive at home plate in .627 seconds at a distance of 46 feet.

 

[jbriggs444]

I make it 39 miles per hour plus a fraction.

The units on the speeds and the units on the distances do not matter. All that matters is their ratio.

If you have $\frac{36}{46}$ of the distance, you need $\frac{36}{46}$ of the speed to break even on the time. $50 \times \frac{36}{46}$ is 39 plus a bit.

 

[gr8tnezz]

I like your method much better Jbriggs. Is this a formula I could use to move through the the little league speed ranges? There’s about a 10 mph range in each age group of average pitches and it bumps up about 5 mph every year until you leave little league. So to mix it up, I could just use your formula substituting different distances as the kids get older and different speeds as they get stronger.

 

[jbriggs444]

I like your method much better Jbriggs. Is this a formula I could use to move through the the little league speed ranges? There’s about a 10 mph range in each age group of average pitches and it bumps up about 5 mph every year until you leave little league. So to mix it up, I could just use your formula substituting different distances as the kids get older and different speeds as they get stronger.

I am happy with the formula I gave. It is not perfect, but should be good enough.

It ignores the fact that the ball slows down in flight. But that's probably OK since the amount it slows down varies with speed and we probably do not want to drown in the complexities of linear drag versus quadratic drag and integrating speed over time.

It also ignores the fact that the ball arches in flight. A slower pitch covers a more curved arc and needs some extra speed because the path it covers is longer.

 

[gr8tnezz]

Yes Jbriggs. For 10 year old Little League it’s perfect! Thank you so much! I will share in my baseball dads forums because this is really good information. Lots of dads take their kids to the batting cages and just guess. I believe in making it realistic to game conditions and this is just the ticket. Thanks again.

 

[A.T.]

It is not perfect, but should be good enough.

I have no knowledge about this topic. But it seems like a major difference to a real pitch is that you don't see the pitcher throwing, just suddenly a ball appearing. Is there some indicator on the machine to at least partially simulate that aspect?

 

[sophiecentaur]

It also ignores the fact that the ball arches in flight. A slower pitch covers a more curved arc and needs some extra speed because the path it covers is longer.

In the same flight time, the ball will fall the same distance so the vertical excursion would be the same in all cases. Although the vertical distance would be the same, the peak would be half way from the pitcher so it could 'look' a bit higher to the batter.
Anyone prepared to do the sums in mph and feet could find the actual difference in the subtended angle. (Not far from a 46/36 ratio in angle if you ignore the trigonometry)

I imagine that the consistency for younger players would not be too good so a batter would be used to a fair range of arrival elevations.

 

[gr8tnezz]

I have no knowledge about this topic. But it seems like a major difference to a real pitch is that you don't see the pitcher throwing, just suddenly a ball appearing. Is there some indicator on the machine to at least partially simulate that aspect?

 

[gr8tnezz]

The best one can do to help with this is to be sure and “show” the batter the ball before placing it in the throwing mechanism. In this way, the batter knows that the ball will soon be on the way. After a few repetitions, the batter’s timing adjusts. It is the same as live action in respect to batter’s gaining an understanding of a pitcher’s motion and release point and developing an ability to see the ball coming out of the hand as early as possible. Not quite the same and there is a loss of fidelity but the batter still uses their vision to anticipate when the ball begins to travel in free space.

 

[gr8tnezz]

In the same flight time, the ball will fall the same distance so the vertical excursion would be the same in all cases. Although the vertical distance would be the same, the peak would be half way from the pitcher so it could 'look' a bit higher to the batter.
Anyone prepared to do the sums in mph and feet could find the actual difference in the subtended angle. (Not far from a 46/36 ratio in angle if you ignore the trigonometry)

I imagine that the consistency for younger players would not be too good so a batter would be used to a fair range of arrival elevations.

 

[gr8tnezz]

Yes, the pitched ball will vary dramatically in height and angle ( dead center of home plate versus off the outside edge for example). The ball may arrive anywhere from knees to high chest and be called a strike as long as it’s close to being “over the plate.” So while trajectory and direction vary, we are assuming top speed is relatively consistent in this scenario. Even high quality pitching machines will have a variance in height and angle but not nearly as inconsistent as a 10 year old kid. So if I could just match the perceived velocity of a 50 mph pitched ball from 46 feet using a pitching machine at 36 feet, I feel that’s my best bet for training.